What is the derivative of (x+5)/(x+1) ?

The derivative of (x+5)/(x+1) is -4/((x+1)^2)

What is the first derivative of (x+5)/(x+1) ?

The first derivative of (x+5)/(x+1) is -4/((x+1)^2)

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derivative of

\frac{x + 5}{x + 1}

- \frac{4}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 5}{x + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x + 5 ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x + 5 )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x + 5) = 1

\frac{d}{d x} (x + 1) = 1

= \frac{1 \cdot ( x + 1 ) - 1 \cdot ( x + 5 )}{( x + 1 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 1 ) - 1 \cdot ( x + 5 )}{( x + 1 ) ^{2}} : - \frac{4}{( x + 1 ) ^{2}}

= - \frac{4}{( x + 1 ) ^{2}}

\int 8 x^{3} + 5 d x

y^{^{'}} + \frac{1}{2} y = 8

\int \frac{3 x ^{2} - 2}{( x ^{3} - 2 x ) ^{7}} d x

\int x^{- p} d x

\frac{\partial}{\partial x} (6 x^{7} y^{5} z^{6})

What is the derivative of (x+5)/(x+1) ?
The derivative of (x+5)/(x+1) is -4/((x+1)^2)
What is the first derivative of (x+5)/(x+1) ?
The first derivative of (x+5)/(x+1) is -4/((x+1)^2)